MATLAB: Element wise conditional evaluation of a function over a meshgrid

Question

I created a 2-D mesh using meshgrid. Now, I want to evaluate a function over this mesh based on the elements of mesh i.e., if the mesh elements are equal then evaluate expression1 else evaluate expression2.

a=linspace(1,2,2);
b=linspace(1,3,3);
[A,B]=meshgrid(a,b)
fact(A,B,0.1)
function f = fact(m,n,lam)
    if m==n
        f=m.*(n+2)+lam;
    else
        f=0;
    end
end

The above just gives me the matrices A and B and 0 from the else statement. I want it to compare the elements of "m" and "n" and evaluate the "if" part if they are the same. I tried using bsxfun(@eq,m,n) instead of m==n. It gives the same result, 0 from the else part. Below is the output.

A =
     1     2
     1     2
     1     2
B =
     1     1
     2     2
     3     3
ans =
     0

Instead, evaluating the following code (no if statement) over the mesh does give me the expected result of the function values over the entire mesh.

a=linspace(1,2,2);
b=linspace(1,3,3);
[A,B]=meshgrid(a,b)
fact(A,B,0.1)
function f = fact(m,n,lam)
        f=m.*(n+2)+lam;
end

gives

A =
     1     2
     1     2
     1     2
B =
     1     1
     2     2
     3     3
ans =
    3.1000    6.1000
    4.1000    8.1000
    5.1000   10.1000

The output I am looking for should look like

3.1000      0
0           8.1000
0           0

Answer 1

f = (A==B) .* (A.*(B+2)+lam);